Viviani, Vincenzo - De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Table of contents

[21.] COROLL.

[22.] MONITVM.

[23.] PROBL. I. PROP. II.

[24.] ALITER.

[25.] ALITER.

[26.] MONITVM.

[27.] LEMMAI. PROP. III.

[28.] PROBL. II. PROP. IV.

[29.] MONITVM.

[30.] PROBL. III. PROP. V.

[31.] PROBL. IV. PROP. VI.

[32.] PROBL. V. PROP. VII.

[33.] MONITVM.

[34.] THEOR. II. PROP. VIII.

[35.] MONITVM.

[36.] LEMMA II. PROP. IX.

[37.] THEOR. III. PROP. X.

[38.] COROLL. I.

[39.] COROLL. II.

[40.] MONITVM.

[41.] THEOR. IV. PROP. XI.

[42.] COROLL.

[43.] MONITVM.

[44.] LEMMA III. PROP. XII.

[45.] ALITER idem breuiùs.

[46.] ITER VM aliter breuiùs, ſed negatiuè.

[47.] COROLL.

[48.] THEOR. V. PROP. XIII.

[49.] COROLL. I.

[50.] COROLL. II.

266

Ambo ſimul latera FL, FH, FIGVRÆ LATERA nuncupantur.

VII.

Recta verò LV æquidiſtans diametro ſectionis FG, vt & recta HL, figuræ
latera ſub tendens dicitur FIGVRAM DETERMINANS, ſeu REGV-
LATRIX, vel REGVLA.

VIII.

Segmenta inſuper diametrorum NF, GF, licet ab ipſo Apollonio dicantur
latitudines, vocentur potius ALTITVDINES, ita vt NF dicatur altitu-
do propria ſemi-applicatæ MN & c.

IX.

Rectæ autem NX, GV, quæ recto lateri FL, ſiue ordinatim ductis æquidi-
ſtant, & inter ſectionis diametrum, & regulam intercipiuntur, vocentur
LATITVDINES, rectangulorum nempe FNX, FGV, quibus ſemi-ap-
plicatarum quadrata NM, GD æqualia ſunt oſtenſa, ita vt XM ſit latitu-
do propria ſemi-applicatæ MN & c. quæ ſemi-applicatæ indifferenter,
ac ſępius dicentur applicatæ, velordinatim ductæ.

COROLL.

HInc patet, in quacunque coni-ſectione, quamlibet ſemi-applicatam
eſſe mediam proportionalem inter propriam altitudinem, propriam-
que latitudinem: hoc eſt quadratum cuiuſcunque ſemi-applicatæ æquari
rectangulo ſub propria altitudine, ac propria latitudine contento: oſtenſum
eſt enim tàm in Parabola, quàm in Hyperbola, vel Ellipſi, vel circulo, qua-
dratum ſemi-applicatæ MN æquari rectangulo FX, quod ſub altitudine
propria FN, ac ſub propria latitudine NX continetur.

HIC animaduertendum eſt in hac propoſitione nos ſub contrariam
com-ſectionem non excluſiſſe, quam Apollonius in eius quinta
primi expendens, circulum eſſe demonſtrauit, quoniam ex eo,
quod ſuperius dictum fuit, elicitur huic etiam competere eandem
Ellipſis proprietatem, videlicet ordinatè applicatarum potentias æquarire-
ctangulis, rectæ lineæ quarto loco inuentæ applicatis, latitudinem habentibus
ea diametri ſegmenta, quæ inter ipſas applicatas, ac ſectionis verticem in-
tercipiuntur, deficientibuſque rectangulis ſimilibus contento ſub tranſuerſo re-
ctoque latere, quæ latera in hac ſub contraria ſectione inter ſe ſunt æqualia, ac
penitùs eadem cum diametro vnius circuli: quamobrem circulus nihil aliud
eſſe videtur quàm Ellipſis æqualium laterum, habens tamen tranſuerſum
latus, quod vicem gerit axis linearum ad ipſum ordinatè ductarum.

Immo ſi noſtri eſſet inſtituti, hic quoque demonſtrare poſſemus non

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